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The ratio of intensities of two waves is 9:1. When they superimpose, the ratio of maximum to minimum intensities will become

  • a)
    4 : 1

  • b)
    3 : 1

  • c)
    2 : 1

  • d)
    9 : 1

Correct answer is option 'A'. Can you explain this answer?
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Given information:
- The ratio of intensities of two waves is 9:1.

To find:
- The ratio of maximum to minimum intensities when the waves superimpose.

Solution:

When two waves superimpose, the resulting intensity is the sum of the individual intensities. Let's assume the intensities of the two waves are I1 and I2, with I1 being 9 times larger than I2.

So, I1 = 9x and I2 = x, where x is a constant.

The maximum intensity occurs when the two waves are in phase and add constructively, resulting in the sum of the intensities. The minimum intensity occurs when the two waves are completely out of phase and cancel each other, resulting in the difference of the intensities.

Maximum Intensity:
When the two waves are in phase, the maximum intensity is the sum of the intensities:

Imax = I1 + I2 = 9x + x = 10x

Minimum Intensity:
When the two waves are completely out of phase, the minimum intensity is the difference of the intensities:

Imin = I1 - I2 = 9x - x = 8x

Ratio of Maximum to Minimum Intensities:
The ratio of maximum to minimum intensities is given by:

Ratio = Imax / Imin = (10x) / (8x) = 10/8 = 5/4

Now, we need to simplify this ratio to the form given in the answer options.

Simplifying the Ratio:
Ratio = 5/4 = (5/4) * (4/4) = 20/16 = 5/4

Comparing this simplified ratio with the answer options, we can see that the correct answer is option A, 4:1.

Answer:
The ratio of maximum to minimum intensities when the waves superimpose is 4:1.
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The ratio of intensities of two waves is 9:1. When they superimpose, the ratio of maximum to minimum intensities will becomea)4 : 1b)3 : 1c)2 : 1d)9 : 1Correct answer is option 'A'. Can you explain this answer?
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